Superconvergent numerical methods based on bivariate spline quasi-interpolant for solving two-dimensional Hammerstein integral equations

M. Sennour and M. Tahrichi

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 846-858

Abstract: In this paper, we develop and analyze two superconvergent numerical methods, the degenerate kernel and Nyström methods, for solving two-dimensional Hammerstein integral equations of the second kind. By employing quadratic and Schoenberg–Marsden spline quasi-interpolants, the proposed methods achieve convergence orders of up to eight for the iterated solutions. Numerical experiments show excellent agreement with the theoretical predictions, confirming the high accuracy and efficiency of the proposed methods.

Keywords: Superconvergent methods; Degenerate kernel method; Nyström method; Spline quasi-interpolant; Hammerstein equations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:846-858

DOI: 10.1016/j.matcom.2026.04.047

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